V. M. Kruglov, “A note to the theory of infinite divisible laws”, Teor. Veroyatnost. i Primenen., 15:2 (1970), 330–336; Theory Probab. Appl., 15:2 (1970), 319

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Teoriya Veroyatnostei i ee Primeneniya, 1970, Volume 15, Issue 2, Pages 330–336 (Mi tvp1833)

This article is cited in 42 scientific papers (total in 42 papers)

Short Communications

A note to the theory of infinite divisible laws

V. M. Kruglov

Moscow

Full-text PDF (358 kB) Citations (42)

Abstract: In the paper, the speed of decreasing of

1 - G (x)

$1-G(x)$ ,

G (- x)

$G(-x)$ is investigated, where

G

$G$ is an infinite divisible distribution function.

Received: 14.11.1968

English version:
Theory of Probability and its Applications, 1970, Volume 15, Issue 2, Pages 319–324
DOI: https://doi.org/10.1137/1115038

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: V. M. Kruglov, “A note to the theory of infinite divisible laws”, Teor. Veroyatnost. i Primenen., 15:2 (1970), 330–336; Theory Probab. Appl., 15:2 (1970), 319–324

Citation in format AMSBIB

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\by V.~M.~Kruglov

\paper A~note to the theory of infinite divisible laws

\jour Teor. Veroyatnost. i Primenen.

\yr 1970

\vol 15

\issue 2

\pages 330--336

\mathnet{http://mi.mathnet.ru/tvp1833}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=272018}

\zmath{https://zbmath.org/?q=an:0301.60014}

\transl

\jour Theory Probab. Appl.

\yr 1970

\vol 15

\issue 2

\pages 319--324

\crossref{https://doi.org/10.1137/1115038}

Linking options:

https://www.mathnet.ru/eng/tvp1833

https://www.mathnet.ru/eng/tvp/v15/i2/p330

Addendum

Addendum: A Note on Infinitely Divisible Distributions
V. M. Kruglov
Teor. Veroyatnost. i Primenen., 1971, 16:2, 401

This publication is cited in the following 42 articles:

S. V. Astashkin, “Sequences of independent functions and structure of rearrangement invariant spaces”, Russian Math. Surveys, 79:3 (2024), 375–457
Franziska Kühn, René L. Schilling, “Maximal inequalities and some applications”, Probab. Surveys, 20:none (2023)
D. Kh. Kazanchyan, “Novye kharakterizatsii brounovskogo dvizheniya”, Vestnik TvGU. Seriya: Prikladnaya matematika, 2018, no. 1, 43–54
Bamdad Hosseini, “Well-Posed Bayesian Inverse Problems with Infinitely Divisible and Heavy-Tailed Prior Measures”, SIAM/ASA J. Uncertainty Quantification, 5:1 (2017), 1024
Golikova N.N., Kruglov V.M., “a Characterisation of the Gaussian Distribution Through the Sample Variance”, Sankhya Ser. A, 77:2 (2015), 330–336
Nina N. Golikova, Victor M. Kruglov, “A Characterisation of the Gaussian Distribution through the Sample Variance”, Sankhya A, 77:2 (2015), 330
S. V. Astashkin, “Approximation of Subspaces of Symmetric Spaces Generated by Independent Functions”, Math. Notes, 96:5 (2014), 625–633
S. V. Astashkin, “Martingale Rosenthal inequalities in symmetric spaces”, Sb. Math., 205:12 (2014), 1720–1740
S. V. Astashkin, “On subspaces generated by independent functions in symmetric spaces with Kruglov property”, St. Petersburg Math. J., 25:4 (2014), 513–527
Kruglov V.M., “A Characterization of the Gaussian Distribution”, Stoch. Anal. Appl., 31:5 (2013), 872–875
S. V. Astashkin, “Rosenthal type inequalities for martingales in symmetric spaces”, Russian Math. (Iz. VUZ), 56:11 (2012), 52–57
Victor M. Kruglov, “A characterization of the convolution of Gaussian and Poisson distributions”, Sankhya A, 74:1 (2012), 1
José E. Figueroa-López, Handbook of Computational Finance, 2012, 61
S. V. Astashkin, F. A. Sukochev, “Independent functions and the geometry of Banach spaces”, Russian Math. Surveys, 65:6 (2010), 1003–1081
S. V. Astashkin, F. A. Sukochev, “Best constants in Rosenthal-type inequalities and the Kruglov operator”, Ann. Probab., 38:5 (2010)
S. V. Astashkin, D. V. Zanin, E. M. Semenov, F. A. Sukochev, “Kruglov Operator and Operators Defined by Random Permutations”, Funct. Anal. Appl., 43:2 (2009), 83–95
S. V. Astashkin, “A Generalized Khintchine Inequality in Rearrangement Invariant Spaces”, Funct. Anal. Appl., 42:2 (2008), 144–147
S. V. Astashkin, “Independent functions in rearrangement invariant spaces and the Kruglov property”, Sb. Math., 199:7 (2008), 945–963
José E. Figueroa-López, “Small-time moment asymptotics for Lévy processes”, Statistics & Probability Letters, 78:18 (2008), 3355
S. V. Astashkin, F. A. Sukochev, “Series of independent mean zero random variables in rearrangement invariant spaces with the Kruglov property”, J. Math. Sci. (N. Y.), 148:6 (2008), 795–809

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Theory of Probability and its Applications

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